The most appropriate rooms for the installment of vanity lights are the rooms in which you will be seen by yourself and by others. Vanity lights are not necessarily for looking at yourself in the mirror, although they are useful there, but also can be set up in places where you want to look your best.
Setting up vanity lights around mirrors is the most common use for the style of lighting. Most often vanity mirrors are found in your bathroom or bedroom, however mirrors hung in a living room can give a very sensible sense of style.
In the bathroom or bedroom the lighting is angled from multiple or large light sources so as to give an even distribution of light. This is the same case with vanity lights in any other part of your home. Keeping the light source close to the mirror in a fashion that will illuminate the subject in front of it will make for and attractive use of the lights.
Mirrors are not particularly necessary for vanity lights, in fact vanity lights can give you and anyone else in the room a more attractive appearance. The purpose is, after all, to give a more attractive form of lighting to you and your room. It is therefore appropriate to use vanity lights in areas where they will accent the beauty of the rooms most important element, you.